The US was in a legal state of war with Germany, Japan, and Italy. Congress has not declared war against Yemen nor have they issued Letters of Marque and Reprisal against anyone. al-Awlaki was never tried or convicted in any US court, even in absentia. Obama claims al-Awlaki is a terrorist and has never provided a shred of evidence. All that is ever issued is a press release. He could just as easily declare Freepers as terrorists. If fact they are laying the ground work for it, conditioning Northcom/Department of Homeland Security and local law enforcement for that day, probably when economy totally crashes and the People go after the crooks responsible.
Second, legitimate al-Qaeda targets in each of those countries are subject to attack pursuant to Congresss 2001 Authorization to Use Military Force after 9/11, which even Vice President Biden has deemed a constitutionally sufficient declaration of war. That disposes of the concern that the executive branch is operating without the imprimatur of Congress. And the president is at all times subject to a variety of laws that constrain his conduct as commander-in-chief. Just because this particular killing is not justiciable (on the facts known to us) does not mean that federal courts cannot hold the president to account for violations of U.S. law.